|
This article is cited in 15 scientific papers (total in 15 papers)
Bi-Hamiltonian ordinary differential equations with matrix variables
A. V. Odesskiia, V. N. Rubtsovbc, V. V. Sokolovd a Brock University, St. Catharines, Canada
b Institute for Theoretical and Experimental Physics, Moscow,
Russia
c LAREMA, CNRS, Université d'Angers, Angers, France
d Landau Institute for Theoretical Physics, RAS, Moscow,
Russia
Abstract:
We consider a special class of Poisson brackets related to systems of
ordinary differential equations with matrix variables. We investigate
general properties of such brackets, present an example of a compatible pair
of quadratic and linear brackets, and find the corresponding hierarchy of
integrable models, which generalizes the two-component Manakov matrix system
to the case of an arbitrary number of matrices.
Keywords:
integrable ordinary differential equation with matrix unknowns,
bi-Hamiltonian formalism, Manakov model.
Received: 07.05.2011
Citation:
A. V. Odesskii, V. N. Rubtsov, V. V. Sokolov, “Bi-Hamiltonian ordinary differential equations with matrix variables”, TMF, 171:1 (2012), 26–32; Theoret. and Math. Phys., 171:1 (2012), 442–447
Linking options:
https://www.mathnet.ru/eng/tmf6912https://doi.org/10.4213/tmf6912 https://www.mathnet.ru/eng/tmf/v171/i1/p26
|
Statistics & downloads: |
Abstract page: | 620 | Full-text PDF : | 215 | References: | 60 | First page: | 22 |
|